Scala analysis: levy-03-malkaus

Ex. 3: Niaz & Faiyaz Ahmed Khan, Mālkãus

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        311.000 cents     311.000000
  2:        501.000 cents     501.000000
  3:        812.000 cents     812.000000
  4:       1007.000 cents    1007.000000
  5:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        193.0000 cents    193.0000
  1:        311.0000 cents    311.0000
  2:        190.0000 cents    190.0000
  3:        311.0000 cents    311.0000
  4:        195.0000 cents    195.0000
  5:        193.0000 cents    193.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 190.00000 cents
  1:   1 193.00000 cents
  1:   1 195.00000 cents
  1:   2 311.00000 cents
  2:   1 388.00000 cents
  2:   2 501.00000 cents
  2:   1 504.00000 cents
  2:   1 506.00000 cents
  3:   1 694.00000 cents
  3:   1 696.00000 cents
  3:   2 699.00000 cents
  3:   1 812.00000 cents
  4:   2 889.00000 cents
  4:   1 1005.00000 cents
  4:   1 1007.00000 cents
  4:   1 1010.00000 cents
Highest number of different intervals for one interval class: 4
Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
         1     2     3     4      5     
 0.0   : 311.0 501.0 812.0 1007.0 1200.0
 311.0 : 190.0 501.0 696.0 889.0  1200.0
 501.0 : 311.0 506.0 699.0 1010.0 1200.0
 812.0 : 195.0 388.0 699.0 889.0  1200.0
 1007.0: 193.0 504.0 694.0 1005.0 1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  190.0000  .. 311.0000 cents      121.00000 cents                    190.00000 cents
  2:  388.0000  .. 506.0000 cents      118.00000 cents                    77.00000 cents
  3:  694.0000  .. 812.0000 cents      118.00000 cents                    188.00000 cents
  4:  889.0000  .. 1010.0000 cents     121.00000 cents                    77.00000 cents
SHOW DATA
Number of notes                     : 5
-- Interval properties --
Smallest interval                   : 190.00000 cents, class 1
Average step (divided formal octave): 240.0000 cents
Largest one step interval           : 311.00000 cents
Average / Smallest step             : 1.263158
Largest / Average step              : 1.295833
Largest / Smallest step             : 1.636842
Median interval of one step         : 195.00000 cents, amount: 1
Most common interval of one step    : 311.00000 cents, amount: 2
Least squares average step          : 250.49091 cents, oct.:  1252.45455 cents
Scale is strictly proper
Scale is a mode of a 1200-tone equal temperament with octave  1200.000 cents
  degrees: 311 501 812 1007 1200
Least number of segments generator  : 601 of 601.000 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 929 of 929.000 cents and inv.
  generated superset size: 111 = 106 more = 2220.000%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABACD
Step pattern size order : DADCB
Scale is a Constant Structure, by a margin of 77.00000 cents
Scale diversity                     : 1.320624
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.601667
Rothenberg efficiency               : 0.480000   redundancy: 0.520000
Efficiency x scale size             : 2.400000
Number of different interval sizes  : 16 = 4.00000 / class
Number of one step interval sizes   : 4
Highest interval variety            : 4
Mean interval variety               : 4.00000 = 4
Median interval variety             : 4
Lowest interval variety             : 4
Smallest interval difference        : 2.00000 cents
Number of recognisable fifths       : 4, average 697.0000 cents
Best fifths form a closed circle
Formal octave complements present   : 1 = 20.0000%
Limited inverse transpositions with margin 121.0000 cents:
 3
-- Rational properties --
FIT/MODE
  5:  1 1 1 1 1  SP B ME I SD: 56.8419 c. M: 92.0000 c. 
  7:  2 1 2 1 1   P M ME S SD: 27.1831 c. M:-45.1429 c.  Thai mode 3
 12:  3 2 3 2 2  SP M ME S SD: 7.9373 c. M: 12.0000 c.  Blues Minor, Raga Malkauns (Malakosh), Raga Hindola, Man Gong, Quan Ming, Yi Ze, Jiao: China, Shegaye: Ethiopia
 19:  5 3 5 3 3  SP M DE S SD: 5.2057 c. M:-9.0526 c. 
 31:  8 5 8 5 5  SP M DE S SD: 1.2506 c. M:-2.2258 c. 
 136: 35 22 35 22 22  SP M DE S SD: 1.4007 c. M: 2.1765 c. 
 139: 36 22 36 23 22  SP   T3   SD: 1.3999 c. M:-3.0719 c. 
 143: 37 23 37 23 23  SP M DE S SD: 1.4448 c. M:-2.4965 c. 
 151: 39 24 39 25 24  SP   T3   SD: 1.2947 c. M:-2.2715 c. 
 154: 40 24 40 25 25  SP   T3 S SD: 1.5238 c. M: 2.2987 c. 
 158: 41 25 41 26 25  SP   T3   SD: 1.4445 c. M:-3.1266 c. 
 161: 42 25 42 26 26  SP   T3 S SD: 1.2332 c. M:-2.0435 c. 
 167: 43 27 43 27 27  SP M DE S SD: 1.3471 c. M: 2.0180 c. 
 170: 44 27 44 28 27  SP   T3   SD: 1.1021 c. M:-2.4118 c. 
 173: 45 27 45 28 28  SP   T3 S SD: 1.0457 c. M: 1.5780 c. 
 185: 48 29 48 30 30  SP   T3 S SD: 1.1361 c. M: 1.5946 c. 
 192: 50 30 50 31 31  SP   T3 S SD: 0.9014 c. M:-1.5000 c. 
 204: 53 32 53 33 33  SP   T3 S SD: 0.7602 c. M: 1.1176 c. 
 216: 56 34 56 35 35  SP   T3 S SD: 0.8819 c. M: 1.4444 c. 
 223: 58 35 58 36 36  SP   T3 S SD: 0.6872 c. M:-1.1076 c. 
 235: 61 37 61 38 38  SP   T3 S SD: 0.5768 c. M: 1.0426 c. 
 254: 66 40 66 41 41  SP   T3 S SD: 0.5572 c. M:-0.8110 c. 
 266: 69 42 69 43 43  SP   T3 S SD: 0.4712 c. M: 0.9850 c. 
 285: 74 45 74 46 46  SP   T3 S SD: 0.4909 c. M: 0.6842 c. 
 297: 77 47 77 48 48  SP   T3 S SD: 0.4265 c. M: 0.9394 c. 
 316: 82 50 82 51 51  SP   T3 S SD: 0.4707 c. M: 0.6709 c. 
 328: 85 52 85 53 53  SP   T3 S SD: 0.4246 c. M: 0.9024 c. 
 374: 97 59 97 61 60  SP        SD: 0.3351 c. M:-0.4866 c. 
 386: 100 61 100 63 62  SP        SD: 0.3666 c. M: 0.6010 c. 
 393: 102 62 102 64 63  SP        SD: 0.3758 c. M:-0.6336 c. 
 405: 105 64 105 66 65  SP        SD: 0.2313 c. M:-0.4074 c. 
 436: 113 69 113 71 70  SP        SD: 0.1597 c. M:-0.3394 c. 
 467: 121 74 121 76 75  SP        SD: 0.1342 c. M:-0.2805 c. 
 498: 129 79 129 81 80  SP        SD: 0.1557 c. M:-0.2289 c. 
 702: 182 111 182 114 113  SP        SD: 0.1105 c. M: 0.1624 c. 
 733: 190 116 190 119 118  SP        SD: 0.0855 c. M: 0.1787 c. 
 1138: 295 180 295 185 183  SP        SD: 0.0681 c. M: 0.1213 c. 
 1169: 303 185 303 190 188  SP        SD: 0.0332 c. M: 0.0590 c. 
 1200: 311 190 311 195 193  SP        SD: 0.0000 c. M:-0.0000 c. 
FIT/HARMONIC
 1 x x x x 2  S SD: 0.0000 cents
 2 x x 3 x 4  S SD: 55.0225 cents
 3 x 4:5 x 6  S SD: 24.1397 cents
 4:5 x 6:7:8  S SD: 34.6765 cents
 5:6:7:8:9:10  H SD: 16.4692 cents
 9:11:12:14:16:18    SD: 12.1165 cents
 10:12:13:16:18:20    SD: 9.6449 cents
 14:17:19:22:25:28    SD: 9.5478 cents
 15:18:20:24:27:30  S SD: 2.4116 cents
 42:50:56:67:75:84    SD: 2.1430 cents
 47:56:63:75:84:94    SD: 2.0912 cents
 57:68:76:91:102:114    SD: 1.3234 cents
 62:74:83:99:111:124    SD: 1.3110 cents
 72:86:96:115:129:144    SD: 1.0687 cents
 77:92:103:123:138:154    SD: 1.0214 cents
 92:110:123:147:165:184    SD: 0.9956 cents
 107:128:143:171:191:214    SD: 0.8163 cents
 117:140:156:187:209:234    SD: 0.7910 cents
 122:146:163:195:218:244    SD: 0.4300 cents
 137:164:183:219:245:274    SD: 0.1655 cents
 289:346:386:462:517:578    SD: 0.1353 cents
 346:414:462:553:619:692    SD: 0.1233 cents
 483:578:645:772:864:966    SD: 0.0750 cents